I don't understand why it needs the pawn at h3.
Remove the black pawn at h3 and you get a mate in two with 6 black pawns rather than 7.
Or place the black pawn at h2 instead of h3, and you get a mate in one move with 7 black pawns.
Without the h3 pawn, white could capture at g2 after black moves from f3 to f2.
Edit: Regarding your second point of getting a mate in one, I think you are misunderstanding the goal here. It's to construct a mating sequence that is as long as possible, and which permits no shortcuts (in this case the position has a mate in 2 but no mate in 1). A shorter sequence can always be constructed by taking the end of a longer one, so that's uninteresting.
You only need 4 pawns to mate:
with white king at e1, black pawns at d3, e2, e3, and f3 have a mate in one. Position is unlikely against a skilled opponent but could happen in an amateur game if white blunders trying to block a possible pawn promotion). This does require white to have an extra piece somewhere to avoid a stalemate.
The original post specified not using the king to help, and I assumed no friendly pieces blocking the checkmated king in. But you can checkmate with either just two pawns or just a king and a pawn if some squares are blocked by unfortunately placed "friendly" pieces.
By "is this position reachable in a standard game?", do you mean "is it possible to reach this position if both players are cooperating to do so?" or "is it plausible to reach this position if both players are playing to win?"
I don't care if players were playing to win or to cooperate, but if exist a sequence of movements that ends up in this position. According to a comment above such a sequence exists, so the answer to my question is yes
One "useless skill" I learned long ago was the knight and bishop mate. I use it any time an opponent refuses to resign. In actuality it helps get better at my "chess vision" for knights and bishops, where my opponent would have just been better off resigning and spending that time working on their game some other way.
For the record, I usually play 20-30 games a day for the past 20-25 years, and it's only come up once without me forcing it. So it really is pretty useless compared to what else you could learn in the same amount of time.
Funny story: as a kid my chess trainer told me how to mate with knight and bishop and I thought it to be "useless". However a short while later I really had this in a "serious" game.. I was able to mate my opponent but only because he made non-optimal moves :)
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[ 3.5 ms ] story [ 79.7 ms ] threadEdit: Regarding your second point of getting a mate in one, I think you are misunderstanding the goal here. It's to construct a mating sequence that is as long as possible, and which permits no shortcuts (in this case the position has a mate in 2 but no mate in 1). A shorter sequence can always be constructed by taking the end of a longer one, so that's uninteresting.
Two pawns would be possible w/ white king on a1, white pawn on a2, white bishop on b1, and black pawns on b2 and a3.
Unlikely positions in a non-cooperative game though.
8/3p4/7k/8/8/4pp2/P3p3/4K3 w - - 0 51
1. Nf3 Nf6 2. Ne5 Ng4 3. Nc6 bxc6 4. h3 g5 5. hxg4 f5 6. Nc3 fxg4 7. Nd5 cxd5 8. e4 dxe4 9. f3 exf3 10. g3 h5 11. Bd3 Bg7 12. Bf5 Be5 13. Qe2 Bxg3+ 14. Kf1 e6 15. Qc4 exf5 16. Qe6+ dxe6 17. d4 Bf2 18. Kxf2 Nd7 19. d5 Ne5 20. Ke3 Nd3 21. Kxd3 h4 22. d6 cxd6 23. b4 Qa5 24. bxa5 Rb8 25. Bb2 Rxb2 26. Rab1 Rxb1 27. c4 h3 28. Rxb1 g3 29. Rb8 g2 30. Rxc8+ Ke7 31. Rxh8 Kd7 32. Ra8 Kc6 33. Rxa7 Kc5 34. Ke3 Kxc4 35. Ra6 g4 36. Ra7 Kb5 37. Ra6 Kxa6 38. Kf2 f4 39. Ke1 Kxa5 40. Kf2 e5 41. Ke1 Kb6 42. Kd2 Kc7 43. Kd1 d5 44. Ke1 d4 45. Kd2 d3 46. Kd1 e4 47. Ke1 d2+ 48. Kf2 Kc8
Here's a mate with an en passant.
For the record, I usually play 20-30 games a day for the past 20-25 years, and it's only come up once without me forcing it. So it really is pretty useless compared to what else you could learn in the same amount of time.
Takeaway: it is really rare but good to know it.
https://lichess.org/analysis/4k3/4P3/3PPP2/8/8/8/8/K7_w_-_-_...